NOTE: unusual time! 

We discuss a class of 5-dimensional supersymmetric non-Lorentzian Lagrangians with an SU(1,3) conformal symmetry. These theories arise from reduction of 6-dimensional CFT's on a comformally compactified spacetime. We use the SU(1,3) Ward identities to find the form of the correlation functions which have a rich structure. Furthermore we show how these can be used to reconstruct  6-dimensional  CFT correlators. 
 

Grothendieck's Quot schemes — moduli spaces of quotient sheaves — are fundamental objects in algebraic geometry, but we know very little about them. This talk will focus on a relatively simple special case: the Quot scheme Quotˡ(E) of length l quotients of a vector bundle E of rank r on a smooth surface S. The scheme Quotˡ(E) is a cross of the Hilbert scheme of points of S (E=O) and the projectivisation of E (l=1); it carries a virtual fundamental class, and if l and r are at least 2, then Quotˡ(E) is singular. I will explain how the ADHM description of Quotˡ(E) provides a conjectural description of the singularities, and show how they can be resolved in the l=2 case. Furthermore, I will describe the relation between Quotˡ(E) and Quotˡ of a quotient of E, prove a functoriality result for the virtual fundamental class, and use it to compute certain tautological integrals over Quotˡ(E).

Successful navigation of the Covid-19 pandemic is predicated on public cooperation with safety measures and appropriate perception of risk, in which emotion and attention play important roles. Signatures of public emotion and attention are present in social media data, thus natural language analysis of this text enables near-to-real-time monitoring of indicators of public risk perception. We compare key epidemiological indicators of the progression of the pandemic with indicators of the public perception of the pandemic constructed from ∼20 million unique Covid-19-related tweets from 12 countries posted between 10th March and 14th June 2020. We find evidence of psychophysical numbing: Twitter users increasingly fixate on mortality, but in a decreasingly emotional and increasingly analytic tone. Semantic network analysis based on word co-occurrences reveals changes in the emotional framing of Covid-19 casualties that are consistent with this hypothesis. We also find that the average attention afforded to national Covid-19 mortality rates is modelled accurately with the Weber–Fechner and power law functions of sensory perception. Our parameter estimates for these models are consistent with estimates from psychological experiments, and indicate that users in this dataset exhibit differential sensitivity by country to the national Covid-19 death rates. Our work illustrates the potential utility of social media for monitoring public risk perception and guiding public communication during crisis scenarios.

Buildings are geometric structures useful in understanding certain classes of groups. In a series of papers written during the 1980s, Ronan and Smith developed the theory of “presheaves on buildings”. By constructing a coefficient system consisting of kP-modules (where P is the stabiliser of a given simplex), and computing the sheaf homology, they proved several results relating the homology spaces with the irreducible G-modules. In this talk we discuss their methods as well as our implementation of the algorithms, which has allowed us to efficiently compute the irreducible representations of some groups of Lie type.

We consider the Plebanski-Demianski family of solutions of minimal gauged supergravity in D=4, which describes an accelerating, rotating and charged black-hole in AdS4. The 4d metric has conical singularities, but we show that it can uplifted to a completely regular solution of D=11 supergravity. We focus on the supersymmetric and extremal case, where the near-horizon geometry is AdS2x\Sigma, where \Sigma is a spindle, or weighted projective space. We argue that this is dual to a d=1, N=(2,0) SCFT which is the IR limit of a 3d SCFT compactified on a spindle. This, in turn, should be realized holographically by wrapping a stack of M2-branes on a spindle. Such construction displays two interesting features: 1) supersymmetry is realized in a novel way, which is not the topological twist, and 2) the R-symmetry of the d=1 SCFT mixes with the U(1) isometry of the spindle, even in the absence of rotation. A similar idea also applies to a class of AdS3x\Sigma solutions of minimal gauged supergravity in D=5.